The new weighted magnitude mean value and variance of fuzzy numbers

Article type: Research Article

Authors: Gong, Yanbing

Affiliations: Department of Information Management, Hohai University, Changzhou, China

Note: [] Corresponding author. Yanbing Gong, Department of Information Management, Hohai University, No. 200 North Jinling Road, Changzhou, China. Tel.: +86 519 8123 0659; E-mail: yanbg79@163.com

Abstract: Fullér and Majlender (Fuzzy Sets and Systems 136 (2003) 363–374) introduced the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. In this paper, we introduce the new notation of lower and upper weighted magnitude mean values of a fuzzy number. The new interval-valued weighted magnitude mean and variance are defined, which differs from the one given by Fullér and Majlender. We will show the relationship of interval-valued weighted magnitude mean and interval-valued weighted possibilistic mean. Furthermore, we shall also introduce the notations of crisp weighted magnitude mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Finally, some comparative examples are used to illustrate the advantage of the proposed weighted magnitude mean value and variance method to order fuzzy numbers.

Keywords: Fuzzy numbers, weighting function, magnitude mean magnitude variance

DOI: 10.3233/IFS-130903

Journal: Journal of Intelligent & Fuzzy Systems, vol. 26, no. 5, pp. 2303-2313, 2014